July  2011, 7(3): 677-697. doi: 10.3934/jimo.2011.7.677

Analysis of globally gated Markovian limited cyclic polling model and its application to uplink traffic in the IEEE 802.16 network

1. 

Department of Telecommunications, Budapest University of Technology and Economics, Budapest

Received  September 2010 Revised  May 2011 Published  June 2011

In this paper we introduce the globally gated Markovian limited service discipline in the cyclic polling model. Under this policy at most K customers are served during the server visit to a station among the customers that are present at the start of the actual polling cycle. Here the random limit K is the actual value of a finite state Markov chain assigned to the actual station. The model enables asymmetric Poisson arrival flows and each station has an individual Markov chain. This model is analyzed and the numerical solution for the mean of the stationary waiting time is provided.
    This model is motivated by the problem of dynamic capacity allocation in Media Access Control of wireless communication networks with Time-Division Multiple Access mechanism. The "globally gated" character of the model is the consequence of the applied reservation mechanisms. In a fixed length frame after allocating the required capacity for the delay sensitive real-time traffic the random remaining capacity is shared among the subscriber stations for the non real-time traffic. The Markovian character of the random limits enables to model the inter frame dependencies of the required real-time capacity at each station individually.
    In the second part of the paper the application of this model to the uplink traffic in the IEEE 802.16 network is discussed.
Citation: Zsolt Saffer, Miklós Telek. Analysis of globally gated Markovian limited cyclic polling model and its application to uplink traffic in the IEEE 802.16 network. Journal of Industrial & Management Optimization, 2011, 7 (3) : 677-697. doi: 10.3934/jimo.2011.7.677
References:
[1]

S. Andreev, Zs. Saffer and A. Anisimov, "Overall Delay Analysis of IEEE 802.16 Network,", Int. Workshop on Multiple Access Comm. (MACOM), (2009). Google Scholar

[2]

O. J. Boxma, H. Levy and U. Yechiali, Cyclic reservation schemes for efficient operation of multiple-queue single-server systems,, Annals of Operations Research, 35 (1992), 187. doi: 10.1007/BF02188704. Google Scholar

[3]

Y.-J. Chang, F.-T. Chien and C.-C. J. Kuo, Delay analysis and comparison of OFDM-TDMA and OFDMA under IEEE 802.16 QoS framework,, IEEE Global Telecomm. Conf. (GLOBECOM), 1 (2006), 1. Google Scholar

[4]

S. Forconi, G. Iazeolla, P. Kritzinger and P. Pillegi, "Modelling Internet Workloads for IEEE 802.16,", Technical Report CS08-03-00, (2008), 08. Google Scholar

[5]

R. Iyengar, P. Iyer and B. Sikdar, Delay analysis of 802.16 based last mile wireless networks,, IEEE Global Telecommunications Conference (GLOBECOM), 5 (2005), 3123. doi: 10.1109/GLOCOM.2005.1578332. Google Scholar

[6]

Zs. Saffer, An introduction to classical cyclic polling model,, Proc. of the 14th Int. Conf. on Analytical and Stochastic Modelling Techniques and Applications (ASMTA'07), (2007), 59. Google Scholar

[7]

Zs. Saffer and M. Telek, Stability of periodic polling system with BMAP arrivals,, European Journal of Operational Research, 197 (2009), 188. doi: 10.1016/j.ejor.2008.05.016. Google Scholar

[8]

Zs. Saffer and M. Telek, Unified analysis of $BMAP$/$G$/$1$ cyclic polling models,, Queueing Systems, 64 (2010), 69. doi: 10.1007/s11134-009-9136-7. Google Scholar

[9]

C. So-In, R. Jain and A.-K. Tamimi, Capacity evaluation for IEEE 802.16e mobile WiMAX,, Journal of Computer Systems, 2010 (2010), 1. doi: 10.1155/2010/279807. Google Scholar

[10]

Standard IEEE 802.16-2009, Part 16: Air Interface for Broadband Wireless Access Systems, Standard for Local and Metropolitan Area Networks,, May 2009., (2009). Google Scholar

[11]

H. Takagi, "Analysis of Polling Systems,", MIT Press, (1986). Google Scholar

[12]

A. Vinel, Y. Zhang, Q. Ni and A. Lyakhov, Efficient request mechanism usage in IEEE 802.16,, IEEE Global Telecommunications Conference (GLOBECOM), 1 (2006), 1. Google Scholar

show all references

References:
[1]

S. Andreev, Zs. Saffer and A. Anisimov, "Overall Delay Analysis of IEEE 802.16 Network,", Int. Workshop on Multiple Access Comm. (MACOM), (2009). Google Scholar

[2]

O. J. Boxma, H. Levy and U. Yechiali, Cyclic reservation schemes for efficient operation of multiple-queue single-server systems,, Annals of Operations Research, 35 (1992), 187. doi: 10.1007/BF02188704. Google Scholar

[3]

Y.-J. Chang, F.-T. Chien and C.-C. J. Kuo, Delay analysis and comparison of OFDM-TDMA and OFDMA under IEEE 802.16 QoS framework,, IEEE Global Telecomm. Conf. (GLOBECOM), 1 (2006), 1. Google Scholar

[4]

S. Forconi, G. Iazeolla, P. Kritzinger and P. Pillegi, "Modelling Internet Workloads for IEEE 802.16,", Technical Report CS08-03-00, (2008), 08. Google Scholar

[5]

R. Iyengar, P. Iyer and B. Sikdar, Delay analysis of 802.16 based last mile wireless networks,, IEEE Global Telecommunications Conference (GLOBECOM), 5 (2005), 3123. doi: 10.1109/GLOCOM.2005.1578332. Google Scholar

[6]

Zs. Saffer, An introduction to classical cyclic polling model,, Proc. of the 14th Int. Conf. on Analytical and Stochastic Modelling Techniques and Applications (ASMTA'07), (2007), 59. Google Scholar

[7]

Zs. Saffer and M. Telek, Stability of periodic polling system with BMAP arrivals,, European Journal of Operational Research, 197 (2009), 188. doi: 10.1016/j.ejor.2008.05.016. Google Scholar

[8]

Zs. Saffer and M. Telek, Unified analysis of $BMAP$/$G$/$1$ cyclic polling models,, Queueing Systems, 64 (2010), 69. doi: 10.1007/s11134-009-9136-7. Google Scholar

[9]

C. So-In, R. Jain and A.-K. Tamimi, Capacity evaluation for IEEE 802.16e mobile WiMAX,, Journal of Computer Systems, 2010 (2010), 1. doi: 10.1155/2010/279807. Google Scholar

[10]

Standard IEEE 802.16-2009, Part 16: Air Interface for Broadband Wireless Access Systems, Standard for Local and Metropolitan Area Networks,, May 2009., (2009). Google Scholar

[11]

H. Takagi, "Analysis of Polling Systems,", MIT Press, (1986). Google Scholar

[12]

A. Vinel, Y. Zhang, Q. Ni and A. Lyakhov, Efficient request mechanism usage in IEEE 802.16,, IEEE Global Telecommunications Conference (GLOBECOM), 1 (2006), 1. Google Scholar

[1]

Zhanqiang Huo, Wuyi Yue, Naishuo Tian, Shunfu Jin. Performance evaluation for the sleep mode in the IEEE 802.16e based on a queueing model with close-down time and multiple vacations. Journal of Industrial & Management Optimization, 2009, 5 (3) : 511-524. doi: 10.3934/jimo.2009.5.511

[2]

Wai-Ki Ching, Sin-Man Choi, Min Huang. Optimal service capacity in a multiple-server queueing system: A game theory approach. Journal of Industrial & Management Optimization, 2010, 6 (1) : 73-102. doi: 10.3934/jimo.2010.6.73

[3]

Andrey Shishkov. Waiting time of propagation and the backward motion of interfaces in thin-film flow theory. Conference Publications, 2007, 2007 (Special) : 938-945. doi: 10.3934/proc.2007.2007.938

[4]

Sin-Man Choi, Ximin Huang, Wai-Ki Ching. Minimizing equilibrium expected sojourn time via performance-based mixed threshold demand allocation in a multiple-server queueing environment. Journal of Industrial & Management Optimization, 2012, 8 (2) : 299-323. doi: 10.3934/jimo.2012.8.299

[5]

Madhu Jain, Sudeep Singh Sanga. Admission control for finite capacity queueing model with general retrial times and state-dependent rates. Journal of Industrial & Management Optimization, 2017, 13 (5) : 1-25. doi: 10.3934/jimo.2019073

[6]

Sangkyu Baek, Bong Dae Choi. Performance of an efficient sleep mode operation for IEEE 802.16m. Journal of Industrial & Management Optimization, 2011, 7 (3) : 623-639. doi: 10.3934/jimo.2011.7.623

[7]

Shunfu Jin, Wuyi Yue, Zsolt Saffer. Analysis and optimization of a gated polling based spectrum allocation mechanism in cognitive radio networks. Journal of Industrial & Management Optimization, 2016, 12 (2) : 687-702. doi: 10.3934/jimo.2016.12.687

[8]

Shunfu Jin, Wuyi Yue. Performance analysis and evaluation for power saving class type III in IEEE 802.16e network. Journal of Industrial & Management Optimization, 2010, 6 (3) : 691-708. doi: 10.3934/jimo.2010.6.691

[9]

Zsolt Saffer, Miklós Telek. Analysis of BMAP vacation queue and its application to IEEE 802.16e sleep mode. Journal of Industrial & Management Optimization, 2010, 6 (3) : 661-690. doi: 10.3934/jimo.2010.6.661

[10]

Shunfu Jin, Wuyi Yue, Xuena Yan. Performance evaluation of a power saving mechanism in IEEE 802.16 wireless MANs with bi-directional traffic. Journal of Industrial & Management Optimization, 2011, 7 (3) : 717-733. doi: 10.3934/jimo.2011.7.717

[11]

Kyung Jae Kim, Jin Soo Park, Bong Dae Choi. Admission control scheme of extended rtPS algorithm for VoIP service in IEEE 802.16e with adaptive modulation and coding. Journal of Industrial & Management Optimization, 2010, 6 (3) : 641-660. doi: 10.3934/jimo.2010.6.641

[12]

Shengzhu Jin, Bong Dae Choi, Doo Seop Eom. Performance analysis of binary exponential backoff MAC protocol for cognitive radio in the IEEE 802.16e/m network. Journal of Industrial & Management Optimization, 2017, 13 (3) : 1483-1494. doi: 10.3934/jimo.2017003

[13]

Willem Mélange, Herwig Bruneel, Bart Steyaert, Dieter Claeys, Joris Walraevens. A continuous-time queueing model with class clustering and global FCFS service discipline. Journal of Industrial & Management Optimization, 2014, 10 (1) : 193-206. doi: 10.3934/jimo.2014.10.193

[14]

Eunju Hwang, Kyung Jae Kim, Bong Dae Choi. Delay distribution and loss probability of bandwidth requests under truncated binary exponential backoff mechanism in IEEE 802.16e over Gilbert-Elliot error channel. Journal of Industrial & Management Optimization, 2009, 5 (3) : 525-540. doi: 10.3934/jimo.2009.5.525

[15]

Hideaki Takagi. Unified and refined analysis of the response time and waiting time in the M/M/m FCFS preemptive-resume priority queue. Journal of Industrial & Management Optimization, 2017, 13 (4) : 1945-1973. doi: 10.3934/jimo.2017026

[16]

Yutaka Sakuma, Atsushi Inoie, Ken’ichi Kawanishi, Masakiyo Miyazawa. Tail asymptotics for waiting time distribution of an M/M/s queue with general impatient time. Journal of Industrial & Management Optimization, 2011, 7 (3) : 593-606. doi: 10.3934/jimo.2011.7.593

[17]

Zsolt Saffer, Wuyi Yue. A dual tandem queueing system with GI service time at the first queue. Journal of Industrial & Management Optimization, 2014, 10 (1) : 167-192. doi: 10.3934/jimo.2014.10.167

[18]

Sofian De Clercq, Koen De Turck, Bart Steyaert, Herwig Bruneel. Frame-bound priority scheduling in discrete-time queueing systems. Journal of Industrial & Management Optimization, 2011, 7 (3) : 767-788. doi: 10.3934/jimo.2011.7.767

[19]

Yoshiaki Kawase, Shoji Kasahara. Priority queueing analysis of transaction-confirmation time for Bitcoin. Journal of Industrial & Management Optimization, 2017, 13 (5) : 1-22. doi: 10.3934/jimo.2018193

[20]

Qing Yang, Shiji Song, Cheng Wu. Inventory policies for a partially observed supply capacity model. Journal of Industrial & Management Optimization, 2013, 9 (1) : 13-30. doi: 10.3934/jimo.2013.9.13

2018 Impact Factor: 1.025

Metrics

  • PDF downloads (8)
  • HTML views (0)
  • Cited by (1)

Other articles
by authors

[Back to Top]